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Some Powers Sum Power (Posted on 2014-03-09) Difficulty: 3 of 5
Determine all possible triplets (A,B,C) of positive integers such that:
                     AB + BC = CA
Prove that there are no others.

No Solution Yet Submitted by K Sengupta    
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re(2): Near Misses Comment 3 of 3 |
(In reply to re: Near Misses by Ady TZIDON)

Indeed

 10   for Tot=2 to 9999
 20    for A=1 to Tot-2
 30      for B=A to Tot-A-1
 40         C=Tot-A-B
 50         if A^B+B^C=C^A then print A;B;C
100      next
110    next
120   next

which checks all A, B and C up to a total of 9999 finds no other solution than 1,1,2 for A,B,C.

Edited on March 9, 2014, 6:55 pm
  Posted by Charlie on 2014-03-09 18:55:13

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